I play golf with friends sometimes, but there are never friendly games.
—Ben Hogan
The true story told in Mark Frost’s The Match starts with wealthy businessman Eddie Lowery bragging at a party on the eve of the 1956 Bing Crosby Clambake. Lowery sponsored two amateur golfers (Ken Venturi and Harvie Ward) who, he claimed, could beat any twosome in a best-ball match. Another businessman, George Coleman, agreed to a big-money bet pitting Lowery’s amateurs against two of Coleman’s friends. The friends turned out to be Ben Hogan and Byron Nelson. Frost weaves details of the terrific match with the dramatic life stories of the four golfers involved.
The match was played at the spectacular and difficult Cypress Point on the Monterey Peninsula in California. Hogan holed out an 85-yard wedge for eagle on the 10th on his way to a course record of 63. Venturi shot 65, while Nelson and Ward were “only” 5 under par with 67s. Hogan and Nelson had a best-ball score of 57 to win by 1.
One of the most dramatic moments of the match came on the par-3 16th hole, one of the most famous holes in golf featuring a 220-yard carry over water to a green perched on a small peninsula reaching into the Pacific Ocean. Hogan and other top golfers often chose to play their tee shots safely to fairway, 40–60 yards short and left of the green. On this day, all four golfers hit drivers. Hogan’s drive found the green; Nelson hit an incredible drive that landed 6 feet from the hole; Venturi hit the green; and, hitting last under all the pressure, Ward launched a frozen rope that landed 5 feet from the hole. Nelson and Ward both made their birdies, and the match blazed on.
An interesting historical footnote to this match is the important role that caddying played. Eddie Lowery, the instigator of the match, had achieved fame as a 10-year-old boy: he was Francis Ouimet’s feisty caddie in the 1913 U.S. Open, which was dramatized in the movie The Greatest Game Ever Played.1 Hogan and Nelson both learned the game as caddies. Amazingly, Nelson and Hogan were caddies at the same country club, Glen Garden Country Club in Fort Worth, Texas. In fact, in 1927 Nelson won the caddie championship at Glen Garden by beating Hogan in a playoff.2 Their careers remained intertwined until Nelson’s early retirement in 1946, only one year after his remarkable eleven straight victories.
In their prime, Hogan and Nelson were considered the best iron players in golf. Almost all golf pro shops display the famous picture of Hogan hitting a 1-iron to the 18th green to win the 1950 U.S. Open. Nelson was immortalized by the USGA when it nicknamed its mechanical swing machine “Iron Byron.” In this chapter, we will see which modern players are especially accurate with irons as we examine approach shot statistics for distances ranging from 50 to 250 yards.
The above story about 220-yard drives may seem quaint. Modern technology has improved distance and accuracy with drivers and other clubs; however, unlike Hogan, nobody hits a 1-iron anymore. The main reason for the loss of this ability is that the defining properties of irons have changed. If you hit your 6-iron about 10 yards farther now than you did 20 years ago, it may be due to better swing mechanics but is probably because your new 6-iron is the same as your old 5-iron. Primarily for marketing reasons (“Gain 10 yards with our revolutionary new club design!”), the average loft of a 6-iron decreased from 36° in the 1960s to 34° in the 1980s to 30° in 2000.3 The 30° 6-iron of 2000 is almost identical to the 30° 5-iron of the 1980s.
Going back a little further in time, we could speculate that Ben Hogan’s 30° club in 1950 may have had a “4” stamped on it. Thus, Hogan’s famous 1-iron may have played like a modern 3-iron. By analogy, a modern 1-iron would be equivalent to an old “∈1”-iron. Even Hogan would have struggled with such a thing.
Before looking at the approach shot statistics, let’s pause to explore the difference that the club loft makes.
How many different swings do you have? Do you have a different swing for each iron? Although some adjustments in swing plane and length of backswing are common, the design of golf clubs allows you to keep essentially the same swing for each iron. As you move from 5-iron to 9-iron, the clubs get progressively shorter and more lofted (i.e., the clubhead points higher above the ground). Both of these changes affect the height and distance of a solid shot, giving you the desired 10-yard gap between irons with little adjustment to your swing.
In table 9.1, a ball is given a fixed launch speed of 120 mph and backspin of 4,200 rpm, and the carry distance is computed. The angles shown correspond to common lofts of the 5-iron through the 9-iron. Notice that the yardage differences from club to club become increasingly larger, with the change in angle from 28° to 31° taking off only about 5 yards, while the change from 37° to 40° takes off over 8 yards. How do you get to a constant 10-yard gap between clubs?
The assumption of equal spin rate and launch speed for each iron, made for the data in table 9.1, is not at all realistic. Spin is a product of the contact between the club and ball. As the club slides under the ball and digs into the ground, the ball rolls up the clubface. The more rolling there is, the more spin the ball has. This is why it is sometimes difficult to get spin on the ball out of the rough: the grass can get in the way and prevent the ball from staying in contact with the club long enough to generate maximum spin. This is also why using “the grease” (e.g., rubbing WD-40 on the clubface) on a driver can reduce a hook or slice: a slicker clubface imparts less spin. Less sidespin, in turn, produces less sideways movement. (However, less backspin also produces less height and possibly less distance.)
Table 9.1 Carry distances for a launch speed of 120 mph with 4,200-rpm backspin, various angles
Think of hitting a ping pong ball with a paddle. If you hit it “square,” or perpendicular, as in figure 9.1a, you will get maximum ball speed and little or no spin. If you chop down with an angled paddle, as in figure 9.1b, you will gain spin but lose ball speed. A similar effect occurs on a golf shot. For a 3-iron, the ball flattens against the clubface at impact and then rebounds off the club at high speed, but the lack of loft allows for little rolling and produces a low spin rate. For a 9-iron, the extra loft produces more of the up the clubface chop in figure 9.1b, and the ball leaves with more spin and less speed. Changes in club loft are automatically accompanied by changes in spin rate and ball speed.
There is another large error in the assumptions behind the table 9.1 data. We assumed that the launch angle of the ball is the same as the loft of the club. The interaction between ball and club also affects the launch angle. There are two sources of energy loss as the ball moves up the clubface. Friction between club and ball slows the ball’s climb up the clubface, and energy is lost as the ball compresses against the club. The net result is that the ball leaves the club at a smaller angle than the loft of the club. Equations for the actual angles are adapted from Jorgensen’s The Physics of Golf.4
Figure 9.1 Square hit versus angled hit: (a) more speed, less spin; (b) less speed, more spin
Table 9.2 Launch angle, ball speed, spin rate, and carry distance for clubs of different loft, adjusted for different club lengths
The more realistic comparison in table 9.2 adjusts the spin rate, launch speed, and launch angle for each club. There is now about a 9-yard difference in distance between irons. In this table, ball speed is measured in mph, spin rate in rpm, and carry distance in yards. A final adjustment shown in the last column is to modify the ball speed to take into account the different lengths of the clubs. As you can see, this has a significant effect on distance and produces a 10-to 11-yard gap in carry distance between clubs.
If you do not have a 10-yard gap between clubs, the problem may be with the clubs. If the manufacturing process was imperfect or the club has been slightly bent, a club may not have the loft that it is supposed to. An audit and adjustment to get your irons properly lofted might improve your game substantially.
The pros, presumably, have their clubs properly fitted and adjusted. How much control do they have over their irons? We first look at tour averages using the ShotLink data from 2007. Other years show similar averages.
In 2007, 840 shots were hit from the fairway at distances between 99 and 100 yards from the hole. These shots stopped a total distance of 190,179 inches from the hole. This means that, from 100 yards out, the pros hit the ball an average of 
inches, or about 18.9 feet, from the hole. Figure 9.2 shows the results of analogous calculations for distances ranging from 4 yards to 300 yards for shots from the fairway.
The points form a fairly smooth curve, but the characteristics of the curve change at about 50 yards. The distance range of 4–50 yards is analyzed in chapter 8. The data points from 50–300 yards seem to curve as part of an upward parabola. This is illustrated in figure 9.3, showing the data from 100–200 yards, with the curve y = 0.0018(x − 100)2 + 0.033(x − 100) + 19.9 superimposed.
This curve illustrates the obvious rule that the closer you are to the hole, the closer you can hit your approach shot. The question is what happens if the distance of the shot doubles. Going from 25 to 50 yards, the pros do not lose that much accuracy. The effects of the increased distance are partially offset by the ability to spin the ball better at 50 yards than at 25 yards. Going from 100 to 200 yards, much more accuracy is lost because of the reduced ability to spin the ball well and the increased effect of wind, awkward lies, and so on.
Figure 9.2 Average distance to the hole from the fairway, 4–300 yards
Figure 9.3 Average distance to the hole from the fairway, 100–200 yards
We saw in chapter 8 that being in the rough strongly affects the pros’ accuracy from short distances. The next set of figures shows the effect of missing the fairway for longer distances. Table 9.3 lists averages from several distances for shots from the fairway, intermediate rough, and primary rough.
The very large values from the primary rough could be partly due to factors not apparent in the data sets. For example, a ball hit into the rough might also be behind a tree, forcing the player to chip sideways instead of going for the green. There are also situations where the golfer lays up to a favorite distance rather than trying to hit the green. Nevertheless, the evidence is that being in the intermediate rough does not cost the pros much. By contrast, the primary rough seems to be a killer. Figure 9.4 shows the data from all distances ranging from 4 to 300 yards.
Table 9.3 Average distance to the hole from different lies
Figure 9.4 Average distance to the hole from different lies, 4–300 yards
The challenge here is to be informative without being encyclopedic. We can rank players on approach shots from any distance range, from both the fairway and the rough. We can rank players by raw distances or by distances compared to Tour averages. With so many choices, it is difficult to know where to start and when to stop.
My choices are fairly Tiger-centric. Table 9.4 shows approach statistics (from ShotLink data) from the fairway in 2009. The small 25-yard distance intervals eliminate the need to compare to Tour averages. You may wonder why I called these tables “Tiger-centric.” Woods made two top tens, but so did Jason Bohn, Brandt Jobe, and Chad Campbell. Rickie Fowler and Tim Clark made three top tens. Tiger has high ranks in all categories (5 out of 6 in the top fifty and all at 71st or better), but there is nothing about the tables that screams “Tiger!” As we will see, in some ways Tiger was by far the best iron player on tour in 2009, but in various categories other players had an extremely good year. It makes sense that no one player could make many of these top ten lists in a given year.
This logic points out the extraordinary nature of Tiger’s 2004 to 2008 seasons. In 2008, Tiger was first or second at every distance from 100 yards to 225 yards except 125–150 yards. This is remarkable consistency and dominance. It is true that 2008 was an injury-shortened season for Tiger, so it is wise to wonder whether those rankings are a one-year fluke. Table 9.5 answers that question decisively.
The context for the rankings is that the statistics are for the 230 golfers who played in the most ShotLink events each year. While a rank of 100 may seem unimpressive, it actually represents an above-average performance. Knowing this, we would find a consistent first-place ranking to be outrageous. With the best 230 golfers going at it, we might expect that five or six of them would have a great year from 100–125 yards, a different five or six would have a great year from 125–150 yards, and so on. For one golfer to dominate multiple distances, as Tiger did, for multiple years is stunning. Notice, however, that Tiger’s ranking are significantly worse from 125–150 yards than from other distances. Perhaps there is a club that gave Tiger trouble.
Before we look at five-year averages from the different distances, here is one more table from the 2009 season. Given the many different players who showed up in table 9.4, is there any way to summarize the statistics from 100–250 yards? Average distance is not reasonable, because the distance gap is too large; comparing a shot from 100 yards to one from 250 yards makes little sense. Instead, let’s go back to a previous method of measuring each shot against the Tour average from that distance. In the 2009 season, the average Tiger Woods shot from the fairway finished 6.23 feet closer to the hole than the average Tour shot from that distance. The top ten ranking against the Tour average in 2009 from the fairway at distances of 100–250 yards is shown in table 9.6. Although the top ten lists in table 9.4 don’t show it, Tiger Woods clearly had the best year hitting close from the fairway in 2009.
Table 9.4 Top ten average approach distances from fairway, 2009
Table 9.7 shows average approach-shot distances for different-length shots for the 2004 through 2008 seasons. The leading averages over the five-year span are significantly higher than the averages for just 2009 (shown in table 9.4). This emphasizes the remarkable nature of all of Tiger’s number 1 yearly rankings. Another way of noting Tiger’s dominance is to see how closely clustered most of the top players’ averages are and then to note the gap from Tiger to number 2.
Table 9.5 Tiger Woods’s rankings, by approach distances from fairway, 2004–2008
We next examine play from the rough for various distance ranges. I have chosen to cut off the lists at 150 yards and to show only the five-year averages.5 At some point, smart players will start laying up to their favorite distance instead of going for the green. Further, for reasons detailed below, a large sample size is more likely to give meaningful information.
Table 9.6 Top ten average approach distances from fairway, 100–250 yards, compared to Tour average, 2009
Table 9.7 Top ten average approach-shot distances from fairway, 2004–2008
Interpretations of the rough statistics are, actually, rough. In table 9.8, no player made the top ten from more than one distance. There are numerous obstacles in the rough which make consistent excellence difficult. A horrendous lie or two can significantly raise your average with only a small number of shots. Also, due to trees, water, or other hazards, there may be a shot or two for which the prudent play is a chip out into the fairway. Such a shot may be a smart play, yes, but your average distance to the hole just took a big hit. For these reasons and others, statistics from the rough reflect more than just the ability to get an iron cleanly on the ball.
In chapter 8, we examined a calculation to determine the location of the ball from the golfer’s perspective. To be precise, we can determine how far long or short the shot is, and we can determine how far off-line the shot is, but we can’t distinguish whether it missed right or left. Here, we use that calculation to learn an interesting fact about where the pros miss.
Table 9.8 Top ten average approach distances from rough, 2004–2008
We first look at the distance that the shots are off-line (left or right). Figure 9.5 plots the means (averages) of the distances off-line for various lengths of shots from the fairway. There is no surprise here: the longer the shot, the more off-line it is. From 170–180 yards out, the last point plotted shows that the average distance off-line is about 20 feet. As with figure 9.3, which shows average distances from the hole, an upward parabola nicely fits the distances beyond 50 yards.6 That is, the general trend for the distance off-line is the same as for the total distance from the hole.
Figure 9.6 shows the standard deviations of the distance off-line from the same locations. Again, the character of the data changes at the 50-yard mark. There is actually a drop in standard deviation from the 50- to 60-yard range to the 60- to 70-yard range. While this could be an artifact of randomness, it may be the result of the pros being able to spin the ball better from distances beyond 50 yards, where the standard deviation is concave up.
Figure 9.5 Means of distance off-line from 10–20 yards, …, 170–180 yards
Figure 9.6 Standard deviations amount off-line from 10–20 yards, …, 170–180 yards
There is a surprise in figure 9.7, which shows the means of the amounts that the shots are short (negative values) or long (positive values). There are two choices here. By looking at absolute values, we can find the average amount that the distance is off. This would be analogous to what I did for figures 9.5 and 9.6. (There, I had no choice; I did not know whether a given shot was left or right.)
The other choice is to compute means of the actual values. In doing this, we are allowing a shot that is 10 feet too long to be cancelled by a shot that is 10 feet too short. The result is shown in figure 9.7. The pros, on the average, consistently come up short; the longer the shots, the shorter they fall. To keep it in perspective, coming up 6 feet short from 180 yards is not a disaster. However, I was not expecting to see the pattern in figure 9.7, where the means seem to oscillate.7
Common advice for nonprofessional golfers is to take more club than you think you need. If I’m 160 yards out, even though I usually hit 8-irons 155–160 yards, I should use a 7-iron. The logic is that most of my irons are less than pure, so I should count on “missing” enough with a 7-iron that it goes 160 yards instead of 170. The advice is probably good. However, I never plan on hitting weak shots and I would hate to “air-mail” a green because I actually made good contact.
Some of the “short syndrome” in figure 9.7 may be due to the same effect. On the rare occasions when a pro mishits an iron, the shot is more likely to come up short than to go long. It is possible that there is more trouble behind a green than in front, in which case staying short may be a smart play. I can only speculate about the cause of the oscillations in figure 9.7, whereby the means go up and down as the distance increases. (There’s probably a good explanation, but I don’t have it.) That mystery remains unsolved.
Figure 9.7 Means of amounts short (−) or long (+) from 10-20 yards, …, 170–180 yards
